Definition:Unit Normal

Definition

Let $S$ be a surface in ordinary $3$-space.

Let $P$ be a point of $S$.

Let $\mathbf n$ be a normal to $S$ at $P$ such that $\mathbf n$ is a unit vector.

Then $\mathbf n$ is known as a unit normal.

Also known as

It is a popular convention to use the hat notation for a unit vector, hence $\mathbf {\hat n}$ can often be seen to denote a unit normal.

Sources

• 1927: C.E. Weatherburn: Differential Geometry of Three Dimensions: Volume $\text { I }$ ... (previous) ... (next): Introduction: Vector Notation and Formulae: Products of Vectors

• Weisstein, Eric W. "Normal Vector." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NormalVector.html